Question

Assume the terminals of a VanderGraaff generator are represented as spheres as shown below. The charge on each terminal is 2.5 uC, (a) What is the voltage between the terminals? (b) How fast will a negative target charge go if it starts from rest at the negative terminal and accelerates across to the positive terminal? (ans. 240,000 V, 2.9x10 m/s) 2. 50cm 1

(ans. 0.158N) (i) what is the power used to push the magnet down at constant velocity? (ans. 3.16 W). Compare the input power with the output power. (j) How much power would be required to run 100 parallel circuits (each circuit is 2 Ohms)? (ans. 316W)

I have the answers but I don't know how to answer them

Answer 1

To find voltage between the terminals consider to two points 'A' and 'B' on the two spheres. (a) Voltage between terminals V = V_A - V_B Now, V_A = Potential at point A = Potential due to sphere (1) + Potential due to sphere (2) therefore V_A = + K theta/R + K(-theta)/37.5 times 10^-2 as R = 12.5, and O_2 A = 37.5 cm Similarly Potential at 'B' V_B = Potential due to sphere (1) + Potential sue to sphere (2) V_B = K(+ theta)/O, B + K(-theta)/R here also, O, B = 37.5 cm \r\n Now V = V_A - V_B V = K theta/R - K theta/O_2 A - K theta/O_1 B + K theta/R V = 2 K theta/R - K theta/O_2 A - K theta/O_1 B V = 2 times 9 times 10^9 times 2.5 times 10^-6/12.5 times 10^-2 - 2 times 9 times 10^9 times 2.5 times 10^-6/37.5 times 10^-2 V = 2 times 9 times 10^9 times 2.5 times 10^-6/10^-2